We report the investigation of the structural stability of Co (1−x) Ni x Si monosilicides for 0 < x < 1. As CoSi crystallizes in the FeSi-type structure (B20) and NiSi is stable in the MnP-type structure (B31), a complete set of samples has been synthesized and a systematic study of phase formation under different annealing conditions were carried out in order to understand the reason of such a structural transition when x goes from 0 to 1. This study has revealed a limit in the solubility of Ni in CoSi B20 structure of about 17.5 at.% and of Co in NiSi B31 phase of about 13 at.%. For 0.35 < x < 0.74 both B20 and B31 phases are present in the sample at there respective limits of solubility. The temperature dependence of the magnetic susceptibility has also been measured revealing diamagnetic behaviors. Optimal structural parameters and phase stability of the solid solution have been investigated using self-consistent full-potential linearized augmented plane wave method (FP-LAPW) based on the density functional theory (DFT). This calculation well predicts the structural instability observed experimentally.